Refinance Rental Property in South Carolina?

[Michael S.]

Anyone know any good SC lenders?

I have a $200,000 rental property in Beaufort, SC that has a $100,000 note on it at 4.875% that I would like to refinance.  In general, I feel like if I can get a rate of 4.5% or lower with <$1000 in ACTUAL closing costs it would be worth it to refinance.  When I type the amounts and zipcode into Bankrate I get zero bids.  I live in CA so this would all have to be done via internet/ phone.  I appreciate any referrals or assistance.  What's the going rate for a straight refinance (no cash out).

Additional Details/ Complications:

-I have had the property for 3 years, continuously rented

-2015 tax return I had $-4500 in losses ($3600 was depreciation, below market rent)

-2016 tax return $-7200 in losses (Hurricane Matthew, depreciation)

-Rent increased from $990 in 2015 to $1250 in late 2016 (market level) 

-740+ personal credit and low personal debt-to-income

I feel like I ought to get a decent rate at 50% LTV, but all the internet lenders seem to get scared off/ overcharge when they hear "investment property." My original loan was a Fannie Mae Homepath, which offered a low down payment for a relatively higher rate.

Thank you!